P.A. Cox - Inorganic chemistry (793955), страница 18
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MO diagram for O2.For more sophisticated purposes (e.g. interpretation of molecular spectra) some refinements need to made to thissimple picture. In particular, the possibility of overlap between a 2s orbital on one atom and the 2pσ on the other canchange the order of MO energies. This does not alter the electron configurations of any species shown in Table 1. but is74SECTION C—STRUCTURE AND BONDING IN MOLECULESTable 1. Electron configurations, bond orders (BO), dissociation energies (D) and bond lengths (R) for some homonuclear diatomicsimportant for some molecules such as C2 (known at high temperatures, e.g. in flames) and for heteronuclear molecules(see Topic C5).Section C—Structure and bonding in moleculesC5MOLECULAR ORBITALS: HETERONUCLEAR DIATOMICSKey NotesBasic principlesHF and BHCORelated topicsOrbitals from atoms of different elements overlap to give unsymmetrical MOs,the bonding MO being more concentrated on the more electronegative atom.The greater the electronegativity difference, the greater the degree oflocalization.In HF the F 2s orbital is too low in energy to be involved significantly inbonding, but in BH both 2s and 2p orbitals on B can contribute to MOs with H1s.
This situation is described as sp hybridization, and leads to bonding andnonbonding MOs with a spatial localization similar to that assumed in VSEPRtheory.When sp hybridization occurs on both atoms in a diatomic the order of MOscan be hard to predict. In CO the highest occupied MO (HOMO) is anonbonding σ orbital resembling a lone-pair on C; the lowest unoccupied MO(LUMO) is a π antibonding orbital.Electronegativity and bond typeMolecular orbitals: homonuclear(B1)diatomics (C4)Basic principlesIn a heteronuclear molecule a bond is formed between different atoms, and the most important difference from thehomonuclear case (Topic C4) is that molecular orbitals (MOs) are no longer shared equally between atoms.
Consider amolecule where each atom has just one valence atomic orbital (AO): an example would be gas-phase LiH with 2s on Liand 1s on H. When MOs are constructed using the LCAO approximation(1)the coefficients c1 and c2 are no longer equal. In LiH the two AOs differ greatly in energy, as H has a higher ionizationenergy and higher electronegativity than Li. If is the AO of lower energy (i.e. of higher ionization energy or greaterelectronegativity; see Topics A5 and B1), then the bonding MO has c2>c1.
The square of each coefficient gives theelectron density in the appropriate AO, and so the bonding MO has more electron density on the more electronegativeatom. Bonding is provided by a combination of two effects: some increase of density between the atoms as in ahomonuclear molecule, together with some electron transfer giving a partially ionic distribution of the form Liδ+ Hδ−.As the electronegativity difference between atoms increases, so does the localization of the MO, making the chargedistribution more ionic.76C5—MOLECULAR ORBITALS: HETERONUCLEAR DIATOMICSFigure 1 shows the MO diagram appropriate to this case.
The antibonding MO is also shown; the electron distributionhere is localized in the reverse direction to that in the bonding MO, but this orbital is not occupied when only twoelectrons are present.As well as providing a description of the transition between purely covalent and purely ionic bonding, the modeldescribed above has a consequence that is important in more complex cases. AOs of very different energy do not mixsignificantly; the resulting MOs are hardly different from the AOs themselves, and it is a good approximation to neglecttheir interaction.HF and BHThe two molecules HF and BH illustrate cases where more orbitals are involved (see Fig. 2).
In HF the fluorine is moreelectronegative, and hence its AOs are lower in the diagram than that of H. It may be assumed that the 2s AO on F istoo far removed in energy from the 1s on H to interact significantly. The bonding and antibonding MOs are formedfrom combinations of H 1s with F 2p. The two pπ AOs on F have no corresponding AO on H to interact with (as 1s is ofσ symmetry; see Topic C4) and so remain nonbonding. The orbital occupancy shown corresponds to a bond order(BO) of one, because the F 2s orbital is also nonbonding.
The bonding orbital is more localized on F and the chargedistribution is Hδ+Fδ−.In BH the electronegativity differences are reversed, and bonding orbitals will be more localized on H. However, 2sand 2pσ AOs on boron are of comparable energy and both can contribute to the bonding. As the number of MOsformed is equal to the number of starting AOs (see Topic C4), the H 1s, and B 2s and 2pσ AOs combine to form threeMOs, of which one is bonding, one approximately nonbonding, and one antibonding. The MOs shown in Fig. 2 may beunderstood in terms of sp hybrid AOs formed on boron by mixing 2s with 2pσ. Two such hybrids are formed, onepointing towards hydrogen and one away.
The former hybrid combines with H 1s giving bonding and antibondingcombinations, whereas the other does not overlap much and is nonbonding. The four valence electrons in BH thus makea bonding pair and a nonbonding pair oriented in opposite directions as predicted in the VSEPR model (Topic C2). Thebond order is one, with the charge distribution Bδ+Hδ− as predicted on electronegativity grounds.Fig. 1. MO diagram for a heteronuclear molecule with one valence s orbital per atom.
The form of the MOs is also shown, with shading indicatingnegative regions of wavefunction.Labeling of MOs in the heteronuclear case follows the same σ or π classification as for homonuclear diatomics but thesubscripts g and u are not given, as there is no center of inversion symmetry (see Topic C3). Different σ and π MOs arelabeled 1, 2, 3,…in order of increasing energy. Normally only valence-shell orbitals are included but occasionally thelabeling includes inner shell orbitals as well. Labeling of the MOs in Fig.
2 follows the normal convention with the MOderived from the inner shell 1s AO on B or F not included. Sometimes the designation σ* or π* is used to distinguishantibonding MOs from the σ or π bonding MOs.SECTION C—STRUCTURE AND BONDING IN MOLECULES77Fig. 2. MO diagrams with the approximate forms of orbitals shown for (a) HF and (b) BH (negative regions shaded).Fig. 3. MO diagram for CO, showing the form of the frontier orbitals 3σ and 2π.COThe MO diagram for CO shown in Fig.
3 illustrates a more complex example, useful for understanding the bonding incarbonyl compounds such as Ni(CO)4 (see Topic H9). Formation of the π MOs is straightforward to understand asthere is only one pair of equivalent AOs on each atom. They combine to form the bonding 1π (concentrated more onoxygen) and the antibonding 2π MOs. The σ MOs are more complex as there are four AOs involved, the 2s and 2pσ oneach atom.
They give four MOs, labeled 1σ–4σ in Fig. 3. Their forms and energies can be understood by imagining thepreliminary formation of two sp hybrids on each atom. The hybrids that point towards each other overlap strongly and78C5—MOLECULAR ORBITALS: HETERONUCLEAR DIATOMICScombine to form the strongly bonding 1σ and strongly antibonding 4σ MOs.
The other two hybrids each point awayfrom the other atom and so do not overlap strongly; they remain almost nonbonding and form ‘lone-pair’ type orbitals,with 2σ localized on oxygen and 3σ on carbon. The 10 valence electrons occupy the MOs as shown. The highestoccupied MO (HOMO) is the ‘carbon lone-pair’ 3σ, and the lowest unoccupied MO (LUMO) the antibonding2π. The HOMO and LUMO are called the frontier orbitals and can be used to understand the interaction of amolecule with other species (see Topics C8 and H9).
Their approximate form in CO is shown in Fig. 3. The bonding inCO comes primarily from two electrons in 1σ and four in 1π, giving a bond order of three as predicted by the valencestructure (Topic C1, Structure 8).Section C—Structure and bonding in moleculesC6MOLECULAR ORBITALS: POLYATOMICSKey NotesLocalized anddelocalized orbitalsDirected valenceMultiple bondingThree-center bondingRelated topicsAlternative bonding descriptions are often possible in polyatomicmolecules, involving either localized (two center) or delocalized(three or more center) molecular orbitals.
The overall electrondistributions predicted may be the same in both models.Directed valence theory uses two-center bonding orbitals, withhybrid combinations of atomic orbitals. Some of the features ofVSEPR are reproduced, but detailed interpretations of bond anglesare different.Multiple bonds are provided by π-type molecular orbitals as withdiatomics.Three-center bonds are necessary for the description of somemolecules. Bridge bonds in diborane are of the three-center twoelectron type, whereas three-center four-electron bonding providesan explanation of some hypervalent molecules.Molecular shapes: VSEPRMolecularorbitals:(C2)heteronucleardiatomics(C5)Localized and delocalized orbitalsWhen the molecular orbital (MO) theory is applied to polyatomic molecules alternative descriptions are possible, asshown in Fig. 1 for the linear gas-phase molecule BeH2.
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